Satellite based positioning method and system for coarse location positioning

ABSTRACT

A satellite based positioning method and system including storing satellite sub-almanac data on a mobile station. Embodiments include using the sub-almanac data to take measurements and calculate a coarse position of the mobile station. Embodiments further include a location server calculating a correction to the coarse position, and the location server determining whether any sub-almanacs used to calculate the coarse position require replacement.

RELATED APPLICATIONS

This patent application is a divisional of U.S. patent application Ser. No. 11/835,300, filed Aug. 7, 2007, entitled Satellite Based Positioning Method And System For Coarse Location Positioning, which is a continuation-in-part of U.S. patent application Ser. No. 09/575,492, filed May 18, 2000, entitled Method and Apparatus for Determining Global Position Using Almanac Information, which are hereby incorporated by reference in their entirety.

FIELD OF INVENTION

The invention relates to satellite based positioning methods and systems, and more particularly, to using stored Global Positioning system (GPS) satellite almanac information to determine the coarse position of a mobile station.

BACKGROUND

Satellite based positioning systems include networks of earth orbiting satellites that constantly transmit geographical position information to receivers. An example of a satellite based positioning system is the Global Positioning System (GPS), which includes a network of earth orbiting satellites (GPS satellites or satellite vehicles). A GPS receiver can be in a fixed position on a base station or location server, or the receiver can be on a mobile unit or station. The GPS receiver and known processing hardware and software are used to receive GPS data from GPS satellites and determine the position of the receiver. GPS technology was first used in military and emergency service applications. As GPS technology becomes more economical and compact, however, it is becoming ever more common in consumer applications. For example, many location based services (LBS) now exist, such as asset tracking, turn-by-turn routing, and friend finding.

The wireless community is investigating procedures and methodologies for LBS that most benefit both the consumer and the provider. The change in focus from emergency to commercial services is characterized by an increased number of users, an increased number of positioning requests per user, and an increase in the accuracy needed to meet various LBS quality of service requirements. As the demand for LBS capabilities grows, the number of users taking advantage of those services will potentially outstrip those transmitting requests for emergency services. Additionally, a number of these services (turn-by-turn routing, for example) involve each user requiring repeated location solutions, which is in contrast to the single position request that characterizes an emergency call. Finally, many of the LBS that are being planned require accuracies far greater than those required for regulatory compliance.

The diversity inherent in proposed LBS offerings presents LBS providers with many choices and challenges. For example, some LBS work better with a mobile station (MS) based approach while others are better served by an MS-assisted solution.

It is desirable to have a satellite based positioning method and system that is able to handle greatly increased LBS system usage while allowing a system operator the flexibility to choose between MS based, MS-assisted, or other approaches. It is further desirable to have a satellite based positioning method and system with the high accuracy required by most LBS. It is desirable to have a satellite based positioning method and system that minimizes the use of network resources while also minimizing the power used by mobile stations.

BRIEF DESCRIPTION OF THE DRAWINGS

The following figures are provided to assist in describing embodiments of the invention, and are not intended to be exclusive or limiting. In the figures, like reference numerals designate like elements.

FIG. 1 is a block diagram of an embodiment of a satellite based positioning system;

FIG. 2 is a flow diagram of a general embodiment of a coarse location positioning method;

FIG. 3 is a flow diagram of another embodiment of a coarse location positioning method;

FIG. 4 is a flow diagram of another embodiment of a coarse location positioning method;

FIG. 5 is a flow diagram of another embodiment of a coarse location positioning method;

FIGS. 6A through 6H illustrate the results of one simulation of an embodiment; and

FIGS. 7A through 7H illustrate the results of another simulation of an embodiment.

DETAILED DESCRIPTION

Embodiments of the invention allow system operators providing LBS to flexibly perform position fixes using various combinations of network resources and mobile station resources. Embodiments of the invention allow system operators to provide LBS to large numbers of subscribers with high accuracy within acceptable time frames.

Embodiments of the invention allow coarse positioning by a mobile station in a satellite based positioning systems, such as the GPS system. Embodiments of the invention provide traditional GPS accuracies while dramatically reducing the bandwidth consumed by similar methods and their required assistance data payloads. Embodiments of coarse location positioning described herein require a minimum amount of transmitted assistance data. While some MS-assisted, techniques rely on acquisition aiding information with a usable lifespan measured in minutes, or on ephemeris data with a lifespan measured in hours, coarse location positioning methods described herein use satellite sub-almanacs that remain usable for many weeks. An almanac is a list of Kepler parameters, e.g., orbit and clock parameters, for all of the satellites operating in the GPS constellation. A sub-almanac contains only the orbit and clock parameters for one satellite.

Complete GPS almanac information is assembled from data broadcast by each satellite in a twelve-second message every thirst seconds, for a total time of twelve minutes. A sub-almanac can be retrieved by receiving any twelve-second message within the twelve minute broadcast. Each sub-almanac is identified by a unique sub-almanac identification. The Kepler parameters are typically not considered accurate enough to be used for precise positioning calculations.

Each satellite continuously transmits its own ephemeris data. Ephemeris data contains satellite position information that is accurate to within five to ten meters of the actual satellite actual location. However, the ephemeris data is only valid for about four hours. The ephemeris data is broadcast from each satellite for eighteen seconds each thirty-second period.

Embodiments described herein allow mobile stations to perform “off-line” processing in which a mobile GPS receiver that has no communication with a network even for several days, can calculate its own coarse position using stored almanac data. This allows the use of significantly less power than conventional methods. The mobile station can communicate the coarse position, and identifications of sub-almanacs used in the coarse position calculation, to a server on the network when communication is restored. At that time, corrections to the position can be made with the help of the network server. In various embodiments, corrections to the position are made at the pseudorange level or at the three-dimensional position vector level with a three-dimensional position correction vector. For example, the corrections can be calculated as a pseudorange correction per satellite. In this case, the sub-almanac based pseudoranges are extracted back from the coarse position, and the pseudorange corrections are applied before recomputing a position with the ephemeris and with accurate time. In another example, the corrections are calculated as a position vector that is calculated over the same satellites used to compute the coarse position.

FIG. 1 is a block diagram of a GPS system 100. The system 100 includes a mobile station 140 (MS) that communicates with a network 110. The network 110, in one embodiment, includes a portable or fixed base station (BS) 130, and a portable or fixed location server 120. The location server 120 acts as a data server to the BS 130, which in turn communicates with the MS 140. The location server 120 has access to GPS data from satellites in view. Typically the location server 120 stores the current ephemeris and almanac data for at least the satellites in view. In the embodiment shown, the location server 120 includes a GPS receiver 121 for receiving the GPS data directly. In other embodiments, the location server does not include a GPS receiver, but receives the GPS data transmitted from another component that has a GPS receiver. The location server 120 further includes a central processing unit (CPU) 122, a memory device 123, and a communications channel interface 124. The communications' channel can include any type of communications channel, such as wired or wireless.

BS 130 includes a central processing unit (CPU) 131, a memory device 132, a wireless transceiver 133, and a communications channel interface 134.

The MS 140 includes a GPS receiver 141, a CPU 142, a, memory device 143 and a wireless transceiver 44. The MS 140 has sub-almanac data stored in the memory 143, although the data may not be a complete almanac.

In other embodiments, the BS 130 also includes GPS capability. Alternatively, complete GPS capability and all of the capability necessary to communicate with the MS 140 is collocated. In general, the MS 140 communicates with some configuration of components on the network 110. The network 110 provides LBS such as asset tracking, in which mobile assets (e.g., taxi cabs) are mobile stations with GPS receivers.

Embodiments of the invention reduce the time to first fix (TTFF) for a GPS mobile station receiver while using minimal power, in part by using GPS sub-almanac data stored on, or sent to, the mobile station to calculate its own coarse position. FIG. 2 is a flow diagram illustrating a general method according to one embodiment. At 200, a coarse positioning session is initiated. The coarse positioning session can be initiated by the MS itself, or the MS may receive a signal initiating the session, such as a positioning request sent or forwarded by the position server or BS. Optionally, the network also transmits a reference position that includes latitude, longitude, and time. The reference position is a precise position of a location that is close enough to the mobile station to be helpful to the mobile station in as an indication of which satellites should be in view and in finding an initial position solution.

At 202, the MS uses stored sub-almanac data along with a reference position (if received) and time estimates, to acquire satellites and take measurements. Taking measurements includes, for example, determining a approximate distance of the mobile station from a particular satellite with some error attributable to time differences. The MS, at 204, uses the measurements, and a satellite position as derived from the sub-almanacs, to calculate a coarse position. At 206, the MS transmits the coarse position to the network along with a list that identifies the particular satellites used in the solution, and the particular sub-almanacs used for each satellite. In some embodiments, the MS transmits a full coarse position. In other embodiments, the MS transmits a position difference between the reference position received from the network, and the coarse position.

At 208, the network derives satellite positions using the current ephemeris. The network then calculates the differences between almanac-derived and ephemeris-derived satellite positions and uses them to create a corrected position for the MS at 210. The network, in various embodiments, can calculate a coarse correction in various ways. For example, the correction can be a pseudo-range correction per satellite. In this case, the sub-almanac pseudoranges are extracted back from the coarse position, and the pseudorange corrections are applied before recomputing the position with the ephemeris, and with time. Alternatively, the coarse position correction can be calculated as a position correction vector that is calculated over the same satellites as those used by the MS to compute the coarse position. The coarse position correction may or may not include differential corrections in different embodiments, where differential corrections account for discrepancies between what the ephemeris predicts and what a reference receiver at a known location sees in the pseudoranges.

At 212, the network determines whether one or more of the sub-almanacs used by the MS contributed an unacceptable level of range error, due for example to the sub-almanacs being too old. If so, the network transmits the latest version of the particular error-causing sub-almanacs to the MS at 214.

A sub-almanac stored at the MS is only replaced when the error associated with the aging data exceeds a specified threshold. This corresponds to a useable life for a sub-almanac that is approximately three weeks to twenty weeks. In one embodiment, an indication of the acceptable level of error is transmitted from the MS to the network. The MS uses the sub-almanacs for both satellite acquisition and for calculating a coarse position.

In various embodiments, the order of the numbered process elements shown in all of the figures, including FIG. 1, may be changed. Alternatively, all of the numbered process elements shown may not be present in various embodiments. For example, in some embodiments, the mobile station may calculate and store a coarse position using stored sub-almanacs, even though the mobile station may not be in contact with the network for some period of time, such as several days. When network contact is restored, the mobile station can immediately transmit its coarse position.

The coarse location positioning method illustrated in FIG. 2 may be applied using a variety of specific schemes. FIG. 3 is a flow diagram illustrating one embodiment of the coarse location positioning method.

At 300, a coarse positioning session is initiated. Optionally, the network also transmits a reference location that includes a latitude, longitude, and time. At 302, the MS uses stored almanac data along with its local position and time estimates, to acquire satellites and take measurements. The MS, at 304, uses the measurements, and satellite positions as derived from the sub-almanacs, to calculate a coarse position. At 306, the MS transmits the coarse position to the network along with a list that identifies the particular satellites used in the solution, and the particular sub-almanac used for each satellite.

At 308, the network calculates an estimated range error for each sub-almanac. At 310, the network determines whether any of the sub-almanacs used by the MS exceed the range error threshold. If none of the sub-almanacs used by the MS exceed the range error threshold, the network calculates the final position solution at 312. If one or more of the sub-almanacs used by the MS exceed the range error threshold, the network transmits replacement sub-almanacs for each of the sub-almanacs exceeding the range error threshold at 314. The network then reissues the position request at 316. In an LBS service characterized by repeated position requests, the single-request path (the path including block 312) is traversed in the vast majority of sessions.

FIG. 4 is a flow diagram illustrating another embodiment of the coarse location positioning method. At 400, a coarse positioning session is initiated. Optionally, the network also transmits a reference location that includes a latitude, longitude, and time. Upon receipt of the position request, at 402, the MS transmits a list of the satellites it will track and the associated sub-almanac identifications to the network. At 404, the network calculates the estimated range errors for each sub-almanac and transmits replacement sub-almanacs for those exceeding the range error threshold. At 406, the MS uses its stored sub-almanacs, including any received replacement sub-almanacs, to acquire satellites and take measurements. At 408, the MS calculates a coarse position using the sub-almanacs. At 410, the MS transmits the coarse position to the network along with a list of the satellites used in the solution and the associated sub-almanac identifications. The network calculates the final position solution at 412 from the information transmitted from the MS.

FIG. 5 is a flow diagram illustrating another embodiment of the coarse location positioning method. At 500, a coarse positioning session is initiated. At 502, the MS, upon receipt of a position request, calculates which satellites it will track. At 504, the MS examines the age of the sub-almanac data associated with each satellite in its proposed tracking list and determines whether the age of any of the sub-almanacs is above a value derived from the predetermined range error threshold. If none of the sub-almanac ages are above the value derived from the range error threshold, as shown at 506, the MS uses its stored sub-almanacs to acquire satellites and take measurements. At 508, the MS calculates a coarse position using the sub-almanacs. At 510, the MS transmits the coarse position to the network along with a list of the satellites used in the solution and the associated sub-almanac identifications. The network calculates the final position solution at 512 from the information transmitted from the MS.

If any sub-almanacs exceed an age threshold, as shown at 514, the MS transmits the list of the satellites it intends to track, the satellites' associated sub-almanac identifications, and the range error threshold to the network. At 516, the network calculates the estimated range errors for each sub-almanac and transmits replacement sub-almanacs for those exceeding the range error threshold. At 518, the MS uses the received replacement sub-almanacs, to acquire satellites and tale measurements. At 508, the MS calculates a coarse position using the sub-almanacs. At 510, the MS transmits the coarse position to the network along with a list of the satellites used in the solution and the associated sub-almanac identifications. The network calculates the final position solution at 512 from the information transmitted from the MS.

In one embodiment, the method for computing and correcting the coarse location includes the following equations.

The MS computes the coarse location using:

Δ{circumflex over (x)} _(A)=(G _(A) ^(T) R ⁻¹ G _(A))⁻¹ G _(A) ^(T) R ⁻¹Δ{circumflex over (ρ)}_(A)  Equation 1

With:

$\begin{matrix} {{{{\Delta \; {\hat{x}}_{A}} = \left\lbrack {\left( {{\hat{\overset{\_}{r}}}_{u} - {\overset{\_}{r}}_{u}} \right)^{T} - {c \cdot B_{u}}} \right\rbrack^{T}}{G_{A} = \begin{bmatrix} {- {\hat{\overset{\_}{1}}}_{1A}^{T}} & 1 \\ \vdots & \vdots \\ {- {\hat{\overset{\_}{1}}}_{n\; A}^{T}} & 1 \end{bmatrix}}{{\hat{\overset{\_}{1}}}_{i\; A} = \frac{{\overset{\_}{r}}_{i\; A} - {\hat{\overset{\_}{r}}}_{u}}{{{\overset{\_}{r}}_{i\; A} - {\hat{\overset{\_}{r}}}_{u}}}}}} & {{{Equations}\mspace{14mu} 2},3,4,{and}} \\ {{{\Delta {\hat{\rho}}_{A}} = \begin{bmatrix} {\Delta \; {\hat{\rho}}_{1\; A}} \\ \vdots \\ {\Delta \; {\hat{\rho}}_{n\; A}} \end{bmatrix}}{{\Delta {\hat{\rho}}_{i\; A}} = {{\hat{\rho}}_{i\; A} - \rho_{i}}}{{\hat{\rho}}_{i\; A} = {{{\hat{\overset{\_}{1}}}_{i\; A}^{T} \cdot \left\lbrack {{\overset{\_}{r}}_{i\; A} - {\hat{\overset{\_}{r}}}_{u}} \right\rbrack} - {c \cdot B_{i\; A}} + {c \cdot {B_{u}.}}}}} & {{{Equations}\mspace{14mu} 5},6,{{and}\mspace{14mu} 7}} \end{matrix}$

Where:

{circumflex over (r)} _(u)=Reference location vector in ECEF coordinates (3.x.1)= r _(u)=Receiver Location vector at reception time in ECEF coordinates (3×1) c=Speed of light in vacuum r _(u)=Almanac-predicted i^(th) satellite location at transmit time in ECEF B_(u)=Almanac-predicted ith satellite clock bias ρ_(i)=Measured pseudorange for ith satellite R=Measurement weighting matrix (n x.n) B_(u)=Receiver clock bias n=Number of satellites used in location solution

The BS corrects coarse location using:

Δ{circumflex over (x)} _(E) ≅Δ{circumflex over (x)} _(A) +P·Δ{circumflex over (ρ)}  Equation 8

With

$\begin{matrix} {{{\hat{\rho}}_{i\; E} = {{{\hat{\overset{\_}{1}}}_{i\; E}^{T} \cdot \left\lbrack {{\overset{\_}{r}}_{i\; E} - {\hat{\overset{\_}{r}}}_{u}} \right\rbrack} - {c \cdot B_{i\; E}} + {c \cdot B_{u}}}}} & {{Equation}\mspace{14mu} 9} \\ {{{\Delta \; \hat{\rho}} = {{\hat{\rho}}_{i\; E} - {\hat{\rho}}_{i\; A}}}} & {{Equation}\mspace{14mu} 10} \\ {{{\Delta \; {\hat{x}}_{E}} = \left\lbrack {\left( {{\hat{\overset{\_}{r}}}_{u} - {\overset{\_}{r}}_{u}} \right)^{T} - {c \cdot B_{u}}} \right\rbrack^{T}}{P = {\left( {G_{E}^{T}R^{- 1}G_{E}} \right)G_{E}^{T}R^{- 1}}}{G_{E} = \begin{bmatrix} {- {\hat{\overset{\_}{1}}}_{1E}^{T}} & 1 \\ \vdots & \vdots \\ {- {\hat{\overset{\_}{1}}}_{n\; E}^{T}} & 1 \end{bmatrix}}} & {{{Equations}\mspace{14mu} 11},12,{13\mspace{14mu} {and}}} \\ {{{\hat{1}}_{i\; E} = \frac{{\overset{\_}{r}}_{i\; E} - {\hat{\overset{\_}{r}}}_{u}}{{{\overset{\_}{r}}_{i\; E} - {\hat{\overset{\_}{r}}}_{u}}}},} & {{Equation}\mspace{14mu} 14} \end{matrix}$

where: r _(IE)=Ephemeris-predicted i^(th) satellite position at transmit time (n×1) B_(IE)=Ephemeris-predicted i^(th) satellite clock bias

Simulations were run to evaluate the accuracy and the sub-almanac data transmission requirements of the coarse location positioning methods described herein. The simulations' were ran using archived sub-almanac and ephemeris data. The simulations were started with a random reference position 10 kilometers from the time position of the unit under test and an up-to-date almanac. Time was moved one week per iteration, and the initial almanac was used to calculate a coarse position at the MS. The coarse position and the sub-almanac identifications for the satellites used in the solution were made available to a simulated location server. The location server, using the ephemeris data appropriate for the simulated week, then calculated the corrected position. At each step, if a satellite's sub-almanac projected an out-of-tolerance range error, a sub-almanac current to that simulated week replaced that satellite's sub-almanac and the replacement was noted. The results of numerous simulations showed that over a 26 week time period, accuracies averaged between 15 and 25 meters. Over the 26 weeks in the simulation, between 6 and 12 satellites required a single sub-almanac replacement.

Results of two simulations are presented in the following figures. The results of one simulation are shown in FIGS. 6A-6H, which illustrate results of a simulation using a 20 kilometer range error replacement threshold.

FIG. 6A illustrates calculated horizontal position error for the simulation. FIG. 6B illustrates the number of sub-almanacs that required replacement in the simulation. FIG. 6C shows the range error estimate for the satellite with the pseudorandom number code (PRN) 3. FIG. 6D shows the range error estimate for the satellite with the pseudorandom number code (PRN) 23. FIG. 6E shows the range error estimate for the satellite with the pseudorandom number code (PRN) 17. FIG. 6F shows the range error estimate for the satellite with the pseudorandom number code (PRN) 26. FIG. 6G shows the range error estimate for the satellite with the pseudorandom number code (PRN) 6. FIG. 6H, shows the range error estimate for the satellite with the pseudorandom number code (PRN) 21.

The results of another simulation are shown in FIGS. 7A-7H, which illustrate results of a simulation using a 50 kilometer range error replacement threshold.

FIG. 7A illustrates calculated horizontal position error for the simulation. FIG. 7B illustrates the number of sub-almanacs that required replacement in the simulation. FIG. 7C shows the range error estimate for the satellite with the pseudorandom number code (PRN) 27. FIG. 7D shows the range error estimate for the satellite with the pseudorandom number code (PRN) 31. FIG. 7E shows the range error estimate for the satellite with the pseudorandom number code (PRN) 8. FIG. 7F shows the range error estimate for the satellite with the pseudorandom number code (PRN) 23. FIG. 7G shows the range error estimate for the satellite with the pseudorandom number code (PRN) 29. FIG. 7H shows the range error estimate for the satellite with the pseudorandom number code (PRN) 7.

To illustrate the downlink bandwidth savings using embodiments of coarse positioning as described herein when compared to a typical acquisition assistance method, two scenarios with their respective bit usages are provided below. Uplink messaging is comparable between the two techniques.

One scenario is turn-by-turn directions. The list below shows particulars used in the comparison between conventional acquisition assistance and coarse location positioning as described herein. Table 1 shows that a reduced number of assistance bits are required when using embodiments of coarse location positioning as described herein.

Number of users: 10 Average length of the session: 20 minutes Usable age for acquisition assistance data: 4 minutes For the coarse location positioning, assume each satellite gets a new sub-almanac during the session (very pessimistic; this would only occur if the user had not performed an LCS session during the previous 3 to 20 weeks) The comparable downlink bandwidth used is:

TABLE 1 Number Total Assistance Bits of Satellites Total Assistance Bits Using Coarse Location In the Solution Using Acquisition Assistance Positioning 4 12,550 7,660 6 18,150 11,420 8 23,750 15,180

Another scenario is asset tracking in which the assets are taxi cabs. The list below shows particulars used in the comparison between conventional acquisition assistance and coarse location positioning as described herein. Table 2 shows that a reduced number of assistance bits are required when using embodiments of coarse location positioning as described herein.

Number of taxis; 15 Average length of the shift: 8 hours Usable age for acquisition assistance data: 4 minutes For coarse location positioning, assume each satellite gets a new sub-almanac during the shift. (again, very pessimistic; this would only occur if the user had not performed an LCS session during the previous 3 to 20 weeks) The comparable downlink bandwidth used in this scenario is:

TABLE 2 Number Total Assistance Bits of Satellites Total Assistance Bits Using Coarse Location in the solution Using Acquisition Assistance Positioning 4 451,800 11,490 6 653,400 17,130 8 855,000 22,770

Various embodiments of the invention have been described with reference to the figures, equations, and tables, none of which are intended to be limiting. Within the scope of the invention, as claimed below, are multiple alternatives not specifically described. For example, the order of operations in the illustrated methods may be changed without departing from the scope of the invention. In addition, the components and their respective functions as shown may be rearranged or reassigned without departing form the scope of the invention. 

1. A satellite based positioning system, comprising: a location server in a network, wherein the location server receives satellite positioning data, including global positioning system (GPS) data; a base station in the network; a mobile station configured to communicate with the base station, wherein the mobile station comprises, a memory that stores satellite sub-almanac data; a central processing unit (CPU) configured to calculate a coarse position using the sub-almanac data; and a transceiver configured to transmit the coarse position to the network.
 2. The system of claim 1, wherein the location server is configured to calculate a correction to the coarse position.
 3. The system of claim 2, wherein the mobile station is further configured to transmit an identification list to the network, wherein the identification list comprises identifications of particular satellites used in calculating the coarse position, and identification of particular sub-almanacs for each of the particular satellites.
 4. The system of claim 3, wherein the location server is configured to determine whether any of the sub-almanacs require replacement, and to transmit any required replacement sub-almanacs to the mobile station.
 5. The system of claim 4, wherein the mobile station is further configured to transmit an indication of an acceptable level of error to the network, and wherein determining whether any of the sub-almanacs requires replacement includes determining whether the acceptable level of error has been exceeded.
 6. The system of claim 1, wherein the mobile station is further configured to receive a reference position, and to use the reference position to calculate the coarse position.
 7. The system of claim 6, wherein transmitting the coarse position comprises transmitting a position difference between the reference position and the coarse position.
 8. The system of claim 5, further comprising the mobile station transmitting an identification list to the network, wherein the identification list comprises identifications of particular satellites used in calculating the coarse position, and identification of particular sub-almanacs for each of the particular satellites.
 9. The system of claim 8, wherein calculating the correction comprises calculating a position correction vector over satellites used to calculate the coarse position.
 10. The system of claim 8, wherein calculating the correction comprises calculating a pseudorange correction for each satellite used to calculate the coarse position.
 11. The system of claim 8, wherein calculating the correction comprises calculating a differential correction, wherein the differential correction accounts for discrepancies between calculation results obtained using ephemeris data, and pseudorange data observed by a reference receiver at a known location. 